therm ow ell design guide 3-39_to_3-44

8/6/2019 Therm Ow Ell Design Guide 3-39_to_3-44

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Thermowell Design Guide

WIKA Instruments Ltd. Thermowell Catalogue, Copyright 2006

There are four critical parameters to consider in thermowell design; Material Compatibility, External Pressure , Steady State Bending Stress and Flow Induced Vibration . For our thermowells, the selection issimplified using this guide*, which is based on the Performance Test Code, ASME/ANSI PTC 19.3.

External Pressure:

When a thermowell is subjected to external pressure the wall thickness must be adequate to support thispressure. The pressure rating of the process connection (i.e. flange, thread, etc.) must also beconsidered. The Maximum Operating Pressure of the thermowell is always the lesser of the two.

The calculation procedure for determining the Maximum External Pressure is defined by the ASMESection VIII Division I. The results of these calculations are presented in Figures 2.2 through 2.9 for selected materials.Select the style and profile of the thermowell.

Options are stepped, tapered, straight, flanged, etc.Obtain the ratio of Bore Diameter (B) to Tip Diameter (V) from Figure 2.1 on page 3-43.Select an appropriate material for the application

See page 3-29 for a guide . Find the corresponding figure for the material selected, refer to pages3-43 and 3-44. If a figure is not available then refer to the applicable code for a calculation procedure.

Determine the Maximum Operating Temperature for the thermowell.This is the highest operating temperature expected during normal service. If this temperature doesnot correspond with a temperature given in the figure, interpolate between nearest temperatures.

Obtain the Maximum External Pressure from the appropriate figure.Maximum External Pressure is the pressure rating of the insertion length.

Obtain the Maximum Pressure Rating of the process connection and compare it to the MaximumOperating Pressure.Maximum Operating Pressure is the highest operating pressure expected during normal service.

Flow Induced Vibration:

When a thermowell is inserted into flowing liquid or gas, circular flow is created downstream of thethermowell. These circular flow patterns are called von Karman (wake) vortices. These vortices breakaway periodically, known as vortex shedding, and cause a regular change in the force on the thermowell.If the regular change, or frequency, of vortex shedding is close to the natural frequency of the thermowell,premature failure of the thermowell can result. This is usually a concern when fluid velocity is high.

This calculation is not required when the thermowell is inserted in fluid that is not moving.

The criteria for an acceptable design is...

f f w

n< 08.

where...f w is the von Karman frequency (Hz), andf n is the natural frequency (Hz) of the thermowell insertion length.

This ratio is known as the Frequency Ratio .

* A more comprehensive Thermowell Design Guide is now available on diskette.Please consult a sales representative for a copy.

Both the Maximum External Pressure and the Process Connection Pressure Ratingmust be higher than the Maximum Operating Pressure for an acceptable design.

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The von Karman Frequency is found using...

f mVA

w =2643600

. v

where...

v is the specific volume of the fluid (ft 3/lbm),m is the mass flow rate of fluid (lbm/hr),V is the tip diameter (inches), and

A is the cross sectional area of the pipe based on inside diameter (ft 2), A = p D2/4/144.

The Natural Frequency is found using...

f K

U E

nf

= 2 ywhere...K f is a constant given in Table 3.3 on page 3-42,U is the insertion length of the thermowell (inches),E is the modulus of elasticity at maximum operating temperature from Table 3.0 on page 3-42 (psi), and

y is the specific weight of the thermowell material (lbf/in 3).

If the Frequency Ratio is greater than or equal to 0.8, the length of the thermowell must be reduced.Recalculate Natural Frequency with the new insertion length U and check the Frequency Ratio again.

Steady State Bending Stress:

When a thermowell is inserted into moving fluid it is subjected to a steady state bending stress. Thisstress is due to the drag force on the thermowell. The longer the thermowell, the higher the stress.

This calculation is not required when the thermowell is inserted in fluid that is not moving. It doesnot account for bending stress due to thermowell weight. A calculation procedure for this casecan be found in any engineering stress analysis text.

The maximum length can be calculated using...

U K V

S K P F f

o

M max

( )=

-+

2 3

1v

where...U max is the maximum insertion length (inches),V f is the fluid velocity (ft/s), V f = mv/A/60,

v is the specific volume of the fluid (ft 3/lbm),S is the allowable stress for the material at design temperature from Table 3.1 on page 3-42 (psi),P o is the maximum operating pressure (psig),F M is the magnification factor (see below), andK 2 , K 3 are constants, see Table 3.2 on page 3-42.

Calculate F M using...

F f f

f f M w n

w n=

-( )

( )

2

21The above calculations for Flow Induced Vibration and Steady State Bending Stress apply only to... tapered or straight thermowells (not stepped), single phase flow, and thermowells inserted perpendicular to the flow.

All calculations assume no corrosion allowance is required.

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Sample CalculationExternal Pressure:

Thermowell Style and Profile ........... Tapered, 1-1/2" Class 1500 Flange (K-style)

Probe Diameter .................................. 1/4"

Bore to Tip Diameter Ratio ............... 0.260/0.75 = 0.35, see figure 2.1 on page 3-43.

Material ................. ................... ........... 316 Stainless Steel (SA-479 Bar)

Design Temperature ........................ 630F

Maximum External Pressure ............ 10,000 psi, from figure 2.5 on page 3-44 at 630F

Flange Pressure Rating .................... 2160 psi (from ASME B16.5)

Maximum Operating Pressure (P o ) 2000 psi

The thermowell is acceptable since both Flange Pressure Rating and Maximum External Pressureare greater than the Maximum Operating Pressure. .

Flow Induced Vibration:

Fluid .................................................... Saturated Water

Specific Volume ( v) ........................... 0.02565 ft 3/lb

Mass Flow Rate ( m )........................... 2.50 x 10 6 lbm/hr

Tip Diameter (V) ................................. 3/4 inch

Pipe ................. .................... ................ 10" NPS Schedule 80

Pipe Inside Diameter (D i).................. 9.562 inches

Insertion Length (U) .......................... 7.5 inches

Kf ........................................................ 2.08, from table 3.3 on page 3-42

Modulus of Elasticity (E) .................. 25.2 x 10 6 psi, from table 3.0 on page 3-42

Specific Weight ( y ) ........................... 0.286 lb/in 3

f w = 126 Hz, f n = 347 Hz, f w /f n = 0.36 The thermowell design is acceptable since f w /f n < 0.80.

Steady State Bending Stress:

K2 ........................................................ 37.5, from table 3.2 on page 3-42

K3 ....................................................... 0.116, from table 3.2 on page 3-42

Specific Volume (n) ........................... 0.02565 ft 3/lb

Allowable Stress (S) .......................... 12,300 psi, from table 3.1 on page 3-42 Maximum Operating Pressure (P o ) 2000 psi

F M = 0.149, V f = 35.7 ft/s, U max = 17.2 inches The thermowell design is acceptable since U max > U.

A Final Note To Our Customers: WIKA Instruments has made every reasonable attempt to validate theabove calculation procedure. However, the responsibility for validation and design lies with the user. Thisinformation is provided as a guide and should not be considered a substitute for professional engineeringdesign. Consult the latest Performance Test Code, ASME/ANSI PTC 19.3, and other applicable codes for a complete calculation procedure.

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3

f

ASME/ANSI PTC 19.3-1974 ASME Section VIII Division I, Section II-D ASME/ANSI B16.5, Pipe Flanges and Flanged FittingsMarks Standard Handbook for Mechanical Engineers

References:

Table 3.0 Modulus of Elasticity (x 10-6

psi)*Temperature, F (C)

Material 70 200 300 400 500 600 700 800 900 1000 1100 1200 1300 1400 1500(21) (93) (150) (200) (260) (315) (370) (425) (480) (540) (590) (650) (700) (760) (815)

Stainless Steel** 28.3 27.6 27 26.5 25.8 25.3 24.8 24.1 23.5 22.8 22.1 21.2 20.2 19.2 18.1

F111Cr Mo 29.7 29 28.5 27.9 27.5 26.9 26.3 25.5 24.8 23.9 23 21.8 20.5 18.9 -Alloy 600 31 30.2 29.9 29.7 29 28.7 28.2 27.6 27 26.4 25.19 25.3 - - -Alloy 800, 825, C276 28.5 27.8 27.4 27.1 26.6 26.4 25.9 25.4 24.8 24.2 23.8 23.2 - - -

* Multiply table values by 1x106

to obtain Modulus of Elasticity in psi. Interpolate between temperatures listed.** Valid for 304, 310S, 316, 321, 347 stainless steel. May also be used for carbon steel (SA-105).

Table 3.1 Allowable Stress (ksi)*Temperature, F (C)

Material to 100 200 300 400 500 600 700 800 900 1000 1100 1200 1300 1400 1500(38) (93) (150) (200) (260) (315) (370) (425) (480) (540) (590) (650) (700) (760) (815)

Carbon Steel (SA-105) 17.5 17.5 17.5 17.5 17.5 17.5 16.6 12 6.5 2.5 - - - - -F11 (SB-182)1Cr Mo 17.5 17.5 17.5 17.5 17.5 17.5 17.5 17.5 13.7 6.3 2.8 1.2 - - -304 (SA-479) 18.8 15.7 14.1 12.9 12.1 11.4 11.1 10.6 10.2 9.8 8.9 6.1 3.7 2.3 1.4316 (SA-479) 18.8 17.7 15.6 14.3 13.3 12.6 12.1 11.7 11.5 11.3 11 7.4 4.1 2.3 1.3310S (SA-479) 18.8 17.6 16.1 15.1 14.3 13.7 13.3 12.9 12.5 9.9 - - - - -321 or 347 (SA-479) 18.8 17.8 16.4 15.3 14.3 13.5 12.9 12.5 12.3 12 6.9 3.6 1.7 0.8 0.3Alloy 600 (SB-166) 20 20 20 20 20 20 19.6 19.1 16 7 3 2 - - -Alloys 800, 825, C276 18.7 18.7 17.9 17.2 16.7 16.3 15.9 15.5 15.1 14.7 13 6.6 2 1.1 0.8

* Multiply table value by 1000 to obtain the Allowable Stress in psi.Source: ASME Section VIII Div. I (1995) and Section II-D (1995). Interpolate between temperatures listed.

Table 3.2 Values for K 2 , K 3Stress Bore Diameter (inches)

Constant 0.260 0.385 0.512 0.702

K2 37.5 42.3 45.5 48.8K3 0.116 0.205 0.336 0.572

Table 3.3 Values for K f Insertion Bore Diameter (inches)

Length (inches) 0.260 0.385 0.512 0.702

2.5 2.06 2.42 2.81 3.694.5 2.07 2.45 2.85 3.807.5 2.08 2.46 2.88 3.86

10.5 2.09 2.47 2.89 3.8916 2.09 2.47 2.90 3.91

24 2.09 2.47 2.90 3.92

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0.1

0.2

0.3

0.4

0.5

0.6

0.1 0.2 0.3 0.4 0.5 0.6

B / V V = 0.500"

V = 0.625"

V = 0.750"

V = 0.875"

V = 1.063"

0

2

4

6

8

10

12

14

16

18

0.2 0.3 0.4 0.5 0.6B/V

M a x i m u m E x t e r n a l P r e s s u r e

, k s i up to 100 F

300 F

500 F

1300 F

1500 F

900 F

1200 F

0

2

4

6

8

10

12

14

0.2 0.3 0.4 0.5 0.6

B/V


, k s i up to 700 F

900 F

950 F

1000 F

1100 F

1200 F

0

2

4

6

8

10

12

14

16

0.2 0.3 0.4 0.5 0.6

B/V


, k s i up to 650 F

700 F

800 F

900 F

1000 F



Figure 2.1Bore Diameter to Tip Diameter Ratio

Figure 2.2Carbon Steel (SA-105)

Figure 2.3F11, 1-1/4% Cr 1/2% Mo (SA-182)

Figure 2.4304 Stainless Steel (SA-479)

S a m p l e

Bore Diameter, inches

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0

2

4

6

8

10

12

14

16

18

0.2 0.3 0.4 0.5 0.6


, k s i

up to 100 F

300 F500 F

1000 F

900 F

0

2

4

6

8

10

12

14

16

18

0.2 0.3 0.4 0.5 0.6B/V


, k s i up to 100 F

500 F

900 F

1100 F

1300 F1500 F

300 F

0

2

4

6

8

10

12

14

16

18

0.2 0.3 0.4 0.5 0.6B/V

M a x i m u m E x t e r n a l P

r e s s u r e

, k s i up to 650 F800 F

950 F

1100 F

1200 F

900 F

1000 F

0

2

4

6

8

10

12

14

16

18

0.2 0.3 0.4 0.5 0.6B/V


, k s i up to 100 F

300 F

1200 F

1300 F

1500 F

500 F

1100 F



Figure 2.5316 Stainless Steel (SA-479)

Figure 2.7321 & 347 Stainless Steel (SA-479)

Figure 2.8Alloy 600 (SB-166)

0

2

4

6

8

10

12

14

16

18

0.2 0.3 0.4 0.5 0.6B/V

M a x i m u m E x t e r n a l P r e s s u r e , k s i up to 200 F

900 F

1100 F

1300 F

1500 F

500 F

1200 F

Figure 2.9Alloy 800 (SB-408), Alloy 825 (SB-425)

Alloy C-276 (SB-574)

Figure 2.6310S Stainless Steel (SA-479)

B/V

S a m p l e

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therm ow ell design guide 3-39_to_3-44

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